SociAl Redistribution

The Mathematics of Solidarity: Why Redistribution is a Necessity

In an ideal world, everyone would have equal resources from birth. In reality, life is a lottery. Some are born into abundance, others into scarcity. More importantly, every human moves through a lifecycle: we are born dependent, we become productive, and we eventually become dependent again.

To optimize well-being, society relies on a redistribution scheme. This isn't just charity; it is a structural necessity where the strong support the vulnerable to ensure stability for everyone.

But how much redistribution is actually needed? The math suggests the number is much higher than most people expect.

The Model: A Village of 100

To understand the economics, let's shrink our complex society down to a single **Village of 100 People**. This allows us to see exactly who needs what, and who is paying the bill.

First, we break down the population based on standard demographics. Note that Healthcare is a massive component of the public sector. 

Key Insight: While 53 people are "working" (Public + Private), only the 40 Private Workers generate the primary market revenue that funds the tax base for the others.

The Calculation: Measuring "Consumption"

To get the real cost, we must look at Resource Consumption. Not everyone consumes the same amount. This creates a "Weighted Cost" for each group.

Step 2: The Resource Bill

The Result: The Production Burden

Here is where the math dictates the economic reality. The village consumes 106.5 units of value to survive. However, this value must be generated primarily by the 40 Private Sector Workers.

The Production Multiplier

If we divide the total needs of the society by the number of people generating the revenue, we find the "Production Multiplier."

(Total Needs) /(Private workers) = 106.5/40= 2.66

This means an active private worker cannot simply earn enough for themselves. To sustain the society described above, a worker must generate roughly 2.7 times their own personal needs.

• 1.0 covers their own consumption.

• 1.7 is transferred (via taxes and fees) to fund the elderly, the sick, and the salaries of the public workforce.

The Redistribution Percentage

This aligns with the tax rates seen in many developed nations. If we look at the "Public Bill" (Elderly + Unemployed + Public Servants), we see that 54 units out of the 106.5 units must be collected and redistributed.

This results in a redistribution rate of roughly 50.7%.

Reality Check: The Tax Breakdown

If the "Public Bill" is 54 Units (out of the Total Pot of 106.5), how is this actually funded in a real economy? Based on typical data from high-redistribution countries (e.g., France, Sweden), the burden is split as follows:

The "Double Dip" Effect

For the Private Worker, this explains the "2.7x" burden:

1. First Dip (Payroll): Before the money hits your bank account, significant taxes (Employer + Employee contributions) are removed to fund the "Labor" share (~25% of total economy).

2. Second Dip (VAT): When you spend your remaining salary, another chunk is removed to fund the "Consumption" share (~15% of total economy).

Conclusion

Redistribution is not merely a political choice; it is a demographic inevitability. Because nearly 20% of the population is elderly (requiring high resources) and 25% is young (producing no resources), the active demographic has no choice but to surrender roughly half of their output to maintain stability for the whole.